In applications, one does typically not have access to measurements of the Gabor transform magnitude on the entire time-frequency plane, however, and one is therefore naturally led to consider the sampled Gabor phase retrieval problem. While it is known that one may invert \(\mathcal {A}\)  for \(S = \mathbb {R}^2\) , much less was known about the inversion of \(\mathcal {A}\)  for discrete sets \(S\) . Recently, however, a series of breakthroughs was presented in the papers [1]}, [2]}, [3]}, [4]}. For the genesis of this paper, the work in [3]} was most important. The authors of [3]} showed that sampled Gabor phase retrieval is unique with \(X = L^4([-B,B])\)  and \(S = \mathbb {Z}\times (4B)^{-1} \mathbb {Z}\) .
